When digital signals are sent across a communication system, it is common to transmit the signals in the form of a modulated carrier signal. After transmission, the received signal must be demodulated to reconstruct the original signal (the content).
Digital modulation schemes use finite numbers of discrete signals. A predefined number of symbols (unique combinations of binary digits) may be assigned for each digital modulation symbol.
Pulse amplitude modulation (PAM) is a modulation scheme which encodes message information in the amplitude of a series of signal pulses. Each digital symbol is encoded as a specific amplitude of the carrier signal. The received signal can then be demodulated by determining which of these set amplitudes the received signal is closest to, and then assigning the symbol corresponding to this set amplitude. Amplitude shift keying (ASK) is a type of PAM which modulates the amplitude of a sinusoidal carrier wave.
Quadrature amplitude modulation (QAM) is a modulation scheme which encodes a digital message by modulating the amplitudes of two carrier waves using ASK. The two carrier waves are sinusoids which are out of phase with each other by 90° (a sine wave and a cosine wave). The two carrier waves are summed and can then be demodulated at the receiving end by separating out the two combined carrier waves and determining the corresponding symbol for the amplitude of each carrier wave.
The set of symbols for a given modulation scheme can be represented by a constellation diagram. For QAM, each symbol (each unique combination of binary digits) can be represented by a complex number representing a position on the complex plane. The sine and cosine carrier waves are modulated by the real and imaginary parts of the complex number for a given symbol to provide the modulated signal for a given symbol. A coherent demodulator can then independently demodulate the two carrier waves to determine the symbol.
Regular QAM constellations (i.e., with equally-spaced points) are widely used in practice due to their relative easiness of implementation (in terms of modulation/demodulation). However, these constellations fall short of achieving the Shannon capacity over Additive White Gaussian Noise (AWGN) channels. A modest performance improvement may be obtained through relaxation of the lattice structure of conventional quadrature amplitude modulation (QAM) constellations by allowing non-equal spacing between neighbouring points. One instance of such constellations is obtained by fitting the distances profile to the cumulative distribution function (CDF) of the normal distribution (e.g., Gaussian-shaped PAM). In order to maintain the In-phase/Quadrature independence, this distances profile fitting may be applied independently over pulse amplitude modulation (PAM) constellations with the resulting QAM constellation being simply the Cartesian product of the underlying PAMs. In a typical scenario, these non-uniform constellations are used in conjunction with an error correcting code (e.g., LDPC or Turbo code).